Study guides › Level 9 · Trigonometry

Exact values of sin, cos and tan

Level 9 · Trigonometry · for questions like “sin 150° = ?”

💡 The idea

On the unit circle (radius 1), cos is the x and sin is the y. Every angle has a reference angle, the sharp angle back to the x-axis, which gives the size. The quadrant gives the sign.

🪜 The steps

1. Find the reference angle (150° → 30°).
2. Look up the value (sin 30° = 1/2).
3. Fix the sign: sin is positive in quadrants I and II, cos in I and IV, tan in I and III.

✏️ Worked examples

1. sin 150°: reference angle 30°, quadrant II (sin is positive), so 1/2.

2. cos 240°: reference angle 60°, quadrant III (cos is negative), so −1/2.

⚠️ Watch out

• “All Students Take Calculus” gives which ones are positive, quadrant by quadrant: All, Sin, Tan, Cos.

🎯 Try these

1. cos 135°
2. tan 300°
3. sin 330°

Answers: 1) −√2/2 2) −√3 3) −1/2

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.